Membrane filters have been widely used in industrial applications to remove contaminants and undesired impurities from the solvent. During the filtration process the membrane internal void area becomes fouled with impurities and as a consequence the filter performance deteriorates, which indeed depends on filter internal structure, particles concentration and flow. The complexity of membrane internal morphology and stochasticity of particles flow make the filtration process and fouling mechanisms a mysterious phenomenon and hard to study. Therefore, mathematical modeling can play a key role in investigating filter fouling and discovering efficient filtration process. So far various mathematical models have been proposed to describe the complexity of membrane structure and stochasticity of particles flow individually but very few focus on both together. In this work, we present an idealized mathematical model, in which a membrane consists of a series of bifurcating pores, which decrease in size as the membrane is traversed and particles are removed from the feed by adsorption within pores (which shrinks them) and stochastic sieving (blocking by large particles). We discuss how filtration efficiency depends on the characteristics of the branching structure.
P. Sanaei, G.W. Richardson, T. Witelski, L.J Cummings, Journal of Fluid Mechanics, 795, 36-59 (2016).
P. Sanaei, L.J Cummings, Journal of Fluid Mechanics, 818, 744-771 (2017).
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